Redo Final Project
Jenny Boynton
5/20/2021
Data Exploration
- I began by glimpsing at my meat consumption data to see what I was working with:
## Rows: 4,480
## Columns: 5
## $ INDICATOR <chr> "MEATCONSUMP", "MEATCONSUMP", "MEATCONSUMP", "MEATCONSUMP",…
## $ SUBJECT <chr> "BEEF", "BEEF", "BEEF", "BEEF", "BEEF", "BEEF", "BEEF", "BE…
## $ TIME <dbl> 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999,…
## $ value_lb <dbl> 0.00, 61.60, 58.22, 58.14, 56.57, 56.28, 60.52, 63.93, 59.0…
## $ country <chr> "Australia", "Australia", "Australia", "Australia", "Austra…- Then I graphed the data in order to see the general trends of meat consumption over time within each country:
Plot 1
- Looking at these graphs I saw that most countries saw an increase in poultry consumption over time, however no other type of meat seemed to follow an obvious pattern.
Plot 2
- I also looked at the same data with the meat values totaled into one sum rather than separated into 4 separate categories:
- This showed me that there seemed to be a slight upward trend in meat consumption in most countries over time, however due to the color scheme it was challenging to tell some countries apart, so I decided to split the graphs apart by continent and adjust the colors used to see if that gave more clarity:
Plot 3
This new graph made it clear that most countries saw an upward trend in meat consumption and that America and Oceania appeared to have the countries with the most meat consumption.
Next I wanted to glimpse at my cardiovascular disease death rate data:
## Rows: 6,468
## Columns: 4
## $ Entity <chr> "Afghanistan", "Afghanistan", "Afghanistan", "Afghanistan",…
## $ Code <chr> "AFG", "AFG", "AFG", "AFG", "AFG", "AFG", "AFG", "AFG", "AF…
## $ Year <dbl> 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999,…
## $ deathrate <dbl> 747.1105, 746.5671, 749.0690, 755.9224, 766.0657, 768.5552,…Plot 4
- I graphed this data to observe the trend over time:
- This showed me that there is a general downwards trend of deaths from CVD over time in most countries.
Plot 5
- Now that I had a general feel for my data I wanted to look at meat consumption vs death rate from cardiovascular disease:
- This graph was hard to identify any obvious patterns so I generated a model and observed the summary table to see if there was anything relevant.
Model 1
##
## Call:
## lm(formula = deathrate ~ value_lb, data = combined_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -221.35 -99.41 -26.08 45.75 462.49
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 301.09744 3.22204 93.45 <2e-16 ***
## value_lb -1.30194 0.09762 -13.34 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 140.7 on 3582 degrees of freedom
## Multiple R-squared: 0.0473, Adjusted R-squared: 0.04704
## F-statistic: 177.9 on 1 and 3582 DF, p-value: < 2.2e-16Looking at cardiovascular mortality rate as a function of consumption quantity, the adjusted R-squared tells me that the graph is only approximately 5% fitted to the regression line, meaning 95% of the variability is unexplained. Looking at the graph this makes sense because the values are all over the place and do not follow a single linear pattern. The p-value tells me it is a statistically significant relationship and the coefficient is slightly negative meaning that generally as consumption of meat goes up, the mortality rate goes down.
I then decided to split up the data by percentage of death rate (high and low) and observe the patterns:
Plot 6
- Immediately the high graph jumped out at me because the bottom value seemed irregular, so I tried only dividing the data into 4 percentages to see if it still had the same issue:
Plot 7
- The issue was even worse, so I observed my data and saw that my first few lowest values had the wrong percentage associated(they were being labeled high). This issue was not affecting any other values, so I filtered out the problem values and tried again:
Plot 6 Redo
- I created a model for this mapped by percentages:
Model 2 - Split into 2 percentages
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -145.75 -98.79 -57.26 70.75 343.09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 382.5737 4.0800 93.769 <2e-16 ***
## value_lb -0.2898 0.1627 -1.781 0.0751 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 131.7 on 1790 degrees of freedom
## Multiple R-squared: 0.001768, Adjusted R-squared: 0.001211
## F-statistic: 3.171 on 1 and 1790 DF, p-value: 0.07513##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -88.694 -34.610 3.392 34.350 72.617
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 168.09117 1.41673 118.647 <2e-16 ***
## value_lb -0.08096 0.03596 -2.251 0.0245 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.66 on 1786 degrees of freedom
## Multiple R-squared: 0.00283, Adjusted R-squared: 0.002272
## F-statistic: 5.069 on 1 and 1786 DF, p-value: 0.02448- The p-value og the higher 50% graph indicated it was not statistically significant, however the lower 50% p-value did indicate it was statistically significant. The r-squared value is not very helpful, which makes sense observing the graphs. In this case, the lower 50% had a slightly negative coefficient. I then analyzed the types of meat to see which contributed to the negative coefficient.
##
## Call:
## lm(formula = deathrate ~ value_lb + SUBJECT, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -88.655 -34.613 2.956 34.099 74.501
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 169.76384 2.39959 70.747 <2e-16 ***
## value_lb -0.12505 0.04469 -2.798 0.0052 **
## SUBJECTPIG -0.61949 2.72867 -0.227 0.8204
## SUBJECTPOULTRY 2.30281 2.84150 0.810 0.4178
## SUBJECTSHEEP -3.27203 2.96047 -1.105 0.2692
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.66 on 1783 degrees of freedom
## Multiple R-squared: 0.004371, Adjusted R-squared: 0.002137
## F-statistic: 1.957 on 4 and 1783 DF, p-value: 0.0986This showed me that poultry is positive and thus is higher when mortality rates are higher, however beef, pig, and sheep have negative coefficients, meaning they are lower when mortality rates are higher.
Next, I decided to go a little deeper into four percentages:
Plot 7 Redo
- I then looked at a model mapped by percentages to see if there was anything statistically relevant:
Model 3 - Split into 4 percentages
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -374.32 -105.57 -13.78 96.15 264.43
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 448.2622 5.2853 84.81 < 2e-16 ***
## value_lb 2.1595 0.2673 8.08 2.09e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 115.7 on 894 degrees of freedom
## Multiple R-squared: 0.06806, Adjusted R-squared: 0.06702
## F-statistic: 65.29 on 1 and 894 DF, p-value: 2.086e-15##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.008 -17.335 0.244 18.520 53.985
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 282.82704 1.01565 278.469 < 2e-16 ***
## value_lb -0.23548 0.03451 -6.823 1.65e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.25 on 894 degrees of freedom
## Multiple R-squared: 0.04949, Adjusted R-squared: 0.04843
## F-statistic: 46.55 on 1 and 894 DF, p-value: 1.647e-11##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.372 -20.098 -0.423 20.444 38.625
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 129.81025 1.14763 113.11 <2e-16 ***
## value_lb 0.02502 0.02750 0.91 0.363
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.75 on 890 degrees of freedom
## Multiple R-squared: 0.0009293, Adjusted R-squared: -0.0001933
## F-statistic: 0.8278 on 1 and 890 DF, p-value: 0.3631##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.405 -16.086 -0.942 15.033 36.448
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 199.74781 0.88239 226.371 <2e-16 ***
## value_lb 0.03754 0.02390 1.571 0.117
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.27 on 894 degrees of freedom
## Multiple R-squared: 0.002753, Adjusted R-squared: 0.001638
## F-statistic: 2.468 on 1 and 894 DF, p-value: 0.1165- This showed me that both high and high-medium had p-values that indicated they were statistically significant, while low-medium and low did not. The high value has a slightly positive coefficient, indicating that for countries with high mortality rates, there is also high meat consumption rates. Whereas, on the other hand, the high medium graph had a slightly negative coefficient indicating the opposite trend; countries with medium high mortality rates are not eating high levels of meat. The r-squared values show a complete lack of explained variability which makes sense when observing the graphs.
R squared values from Model 2:
## # A tibble: 1 x 4
## high `high-medium` low `low-medium`
## <dbl> <dbl> <dbl> <dbl>
## 1 0.0681 0.0495 0.000929 0.00275- The r-squared values show a complete lack of explained variability which makes sense when observing the graphs.
Model 4
- I then wanted to further observe the statistically significant graphs and see which types of meat followed which pattern, so I generated a new model for each to see:
##
## Call:
## lm(formula = deathrate ~ value_lb + SUBJECT, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -401.70 -107.32 -12.14 98.98 247.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 432.1566 9.2703 46.617 < 2e-16 ***
## value_lb 2.5145 0.2871 8.757 < 2e-16 ***
## SUBJECTPIG 13.6762 10.9988 1.243 0.21404
## SUBJECTPOULTRY -1.1322 10.8881 -0.104 0.91720
## SUBJECTSHEEP 32.7304 11.5110 2.843 0.00457 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 115.2 on 891 degrees of freedom
## Multiple R-squared: 0.07925, Adjusted R-squared: 0.07512
## F-statistic: 19.17 on 4 and 891 DF, p-value: 3.846e-15##
## Call:
## lm(formula = deathrate ~ value_lb + SUBJECT, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.42 -17.81 -0.42 18.45 55.85
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 284.33361 1.75622 161.901 < 2e-16 ***
## value_lb -0.26512 0.03656 -7.251 8.98e-13 ***
## SUBJECTPIG -0.37597 2.19441 -0.171 0.8640
## SUBJECTPOULTRY 0.90278 2.19733 0.411 0.6813
## SUBJECTSHEEP -4.30571 2.27275 -1.894 0.0585 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.22 on 891 degrees of freedom
## Multiple R-squared: 0.05572, Adjusted R-squared: 0.05148
## F-statistic: 13.14 on 4 and 891 DF, p-value: 2.087e-10- The p-value maintains that both graphs are statistically significant, and the coefficients of each follow an opposite pattern; beef, pig, and predominantly sheep all have positive coefficients for the high graph, indicating higher levels of consumption when mortality rates are higher. Poultry, on the other hand, has a negative coefficient so when mortality rates are higher, poultry consumption levels are lower. Whereas, for the high-medium graph beef, pig, and sheep all have negative coefficients, and poultry has a positive coefficient.
Model 5
- Then I wanted to see if the problem values were impacting my original model for my combined data (Model 1) so I generated a new summary table
##
## Call:
## lm(formula = deathrate ~ value_lb, data = combined_data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -221.58 -99.44 -26.12 45.63 462.29
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 301.33661 3.22174 93.53 <2e-16 ***
## value_lb -1.30293 0.09759 -13.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 140.7 on 3578 degrees of freedom
## Multiple R-squared: 0.04745, Adjusted R-squared: 0.04718
## F-statistic: 178.2 on 1 and 3578 DF, p-value: < 2.2e-16- These results had the slightest differences from Model 1, but not enough to have an impact on the results.
Model 6 - Split by type of meat (Beef, Pig, Poultry, Sheep)
- Then I divided by subject to see the impact of each type of meat:
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -204.61 -102.42 -25.31 40.92 453.26
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 297.5667 7.3465 40.505 < 2e-16 ***
## value_lb -0.9795 0.2136 -4.586 5.17e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 142.6 on 893 degrees of freedom
## Multiple R-squared: 0.02301, Adjusted R-squared: 0.02191
## F-statistic: 21.03 on 1 and 893 DF, p-value: 5.168e-06##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -215.44 -98.31 -31.48 53.27 454.03
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 314.5354 7.0927 44.346 < 2e-16 ***
## value_lb -1.9380 0.2433 -7.967 4.94e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 139.4 on 893 degrees of freedom
## Multiple R-squared: 0.06636, Adjusted R-squared: 0.06532
## F-statistic: 63.47 on 1 and 893 DF, p-value: 4.938e-15##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -201.04 -89.15 -27.30 40.09 435.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 346.7816 6.9016 50.25 <2e-16 ***
## value_lb -2.0599 0.1471 -14.00 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 130.6 on 893 degrees of freedom
## Multiple R-squared: 0.1801, Adjusted R-squared: 0.1792
## F-statistic: 196.1 on 1 and 893 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -193.21 -102.62 -35.15 50.36 444.25
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 272.6206 5.6404 48.333 <2e-16 ***
## value_lb -0.1195 0.5060 -0.236 0.813
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 144.3 on 893 degrees of freedom
## Multiple R-squared: 6.247e-05, Adjusted R-squared: -0.001057
## F-statistic: 0.05579 on 1 and 893 DF, p-value: 0.8133Only the first three were statistically significant, and each showed a slightly negative coefficient.
Then I looked at each additional variable to see which one had the biggest impact:
Model 7 - Variables: meat value per pound & country
##
## Call:
## lm(formula = deathrate ~ value_lb + country, data = combined_data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -168.751 -31.364 -3.701 29.060 122.822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 253.62456 4.56318 55.581 < 2e-16 ***
## value_lb -0.22063 0.03803 -5.802 7.13e-09 ***
## countryAustralia -78.91967 6.05109 -13.042 < 2e-16 ***
## countryBrazil -6.83437 6.05302 -1.129 0.25894
## countryCanada -91.73913 6.04771 -15.169 < 2e-16 ***
## countryChile -76.36536 6.06354 -12.594 < 2e-16 ***
## countryChina 41.18282 6.10022 6.751 1.71e-11 ***
## countryColombia -61.06501 6.11427 -9.987 < 2e-16 ***
## countryEgypt 295.60460 6.17212 47.894 < 2e-16 ***
## countryEthiopia 33.88984 6.23227 5.438 5.76e-08 ***
## countryIndia 35.90502 6.23700 5.757 9.30e-09 ***
## countryIndonesia 85.93903 6.21242 13.833 < 2e-16 ***
## countryIran 70.20243 6.14302 11.428 < 2e-16 ***
## countryIsrael -78.79616 6.04724 -13.030 < 2e-16 ***
## countryJapan -132.50570 6.16399 -21.497 < 2e-16 ***
## countryKazakhstan 337.46358 6.09759 55.344 < 2e-16 ***
## countryMexico -82.66179 6.08997 -13.573 < 2e-16 ***
## countryNew Zealand -52.64711 6.04754 -8.706 < 2e-16 ***
## countryNigeria -36.45828 6.22250 -5.859 5.08e-09 ***
## countryNorway -61.91149 6.07471 -10.192 < 2e-16 ***
## countryPakistan 181.15765 6.19836 29.227 < 2e-16 ***
## countryParaguay -17.52419 6.08099 -2.882 0.00398 **
## countryPeru -119.54058 6.11981 -19.533 < 2e-16 ***
## countryPhilippines 100.97308 6.14715 16.426 < 2e-16 ***
## countryRussia 347.06619 6.08618 57.025 < 2e-16 ***
## countrySouth Africa 11.78248 6.09662 1.933 0.05336 .
## countrySwitzerland -92.80526 6.06148 -15.311 < 2e-16 ***
## countryThailand -86.65175 6.15419 -14.080 < 2e-16 ***
## countryTurkey -16.11479 6.15448 -2.618 0.00887 **
## countryUkraine 354.72083 6.11609 57.998 < 2e-16 ***
## countryUnited Kingdom -52.24032 6.05963 -8.621 < 2e-16 ***
## countryUnited States -46.55132 6.06122 -7.680 2.04e-14 ***
## countryVietnam 34.98040 6.12522 5.711 1.22e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 45.25 on 3547 degrees of freedom
## Multiple R-squared: 0.9023, Adjusted R-squared: 0.9014
## F-statistic: 1024 on 32 and 3547 DF, p-value: < 2.2e-16Model 8 - Variables: meat value per pound & country & subject
##
## Call:
## lm(formula = deathrate ~ value_lb + country + SUBJECT, data = combined_data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -165.959 -30.992 -3.496 28.516 121.806
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 258.85292 4.92290 52.581 < 2e-16 ***
## value_lb -0.31804 0.04558 -6.978 3.57e-12 ***
## countryAustralia -78.35709 6.04271 -12.967 < 2e-16 ***
## countryBrazil -7.51938 6.04548 -1.244 0.21365
## countryCanada -91.95878 6.03785 -15.230 < 2e-16 ***
## countryChile -77.50831 6.06062 -12.789 < 2e-16 ***
## countryChina 39.12506 6.11327 6.400 1.76e-10 ***
## countryColombia -63.38024 6.13340 -10.334 < 2e-16 ***
## countryEgypt 292.43837 6.21609 47.045 < 2e-16 ***
## countryEthiopia 30.02691 6.30173 4.765 1.97e-06 ***
## countryIndia 31.99240 6.30844 5.071 4.15e-07 ***
## countryIndonesia 82.29205 6.27350 13.117 < 2e-16 ***
## countryIran 67.43243 6.17453 10.921 < 2e-16 ***
## countryIsrael -78.89713 6.03716 -13.069 < 2e-16 ***
## countryJapan -134.72447 6.18043 -21.799 < 2e-16 ***
## countryKazakhstan 335.45776 6.10949 54.908 < 2e-16 ***
## countryMexico -84.50960 6.09857 -13.857 < 2e-16 ***
## countryNew Zealand -52.46100 6.03761 -8.689 < 2e-16 ***
## countryNigeria -40.21634 6.28784 -6.396 1.80e-10 ***
## countryNorway -63.39349 6.07667 -10.432 < 2e-16 ***
## countryPakistan 177.67117 6.25349 28.412 < 2e-16 ***
## countryParaguay -19.16643 6.08568 -3.149 0.00165 **
## countryPeru -121.95006 6.14134 -19.857 < 2e-16 ***
## countryPhilippines 98.14346 6.18045 15.880 < 2e-16 ***
## countryRussia 345.30225 6.09313 56.671 < 2e-16 ***
## countrySouth Africa 9.79606 6.10810 1.604 0.10885
## countrySwitzerland -93.87408 6.05765 -15.497 < 2e-16 ***
## countryThailand -89.57996 6.19049 -14.471 < 2e-16 ***
## countryTurkey -19.04702 6.19091 -3.077 0.00211 **
## countryUkraine 352.37422 6.13601 57.427 < 2e-16 ***
## countryUnited Kingdom -53.23776 6.05499 -8.792 < 2e-16 ***
## countryUnited States -45.49246 6.05727 -7.510 7.42e-14 ***
## countryVietnam 32.48245 6.14907 5.282 1.35e-07 ***
## SUBJECTPIG -1.33274 2.14411 -0.622 0.53426
## SUBJECTPOULTRY 3.23211 2.18524 1.479 0.13921
## SUBJECTSHEEP -6.48524 2.32907 -2.784 0.00539 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 45.18 on 3544 degrees of freedom
## Multiple R-squared: 0.9027, Adjusted R-squared: 0.9017
## F-statistic: 939.3 on 35 and 3544 DF, p-value: < 2.2e-16Model 9 - Variables: meat value per pound & country & subject & year
##
## Call:
## lm(formula = deathrate ~ value_lb + country + SUBJECT + Year,
## data = combined_data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -174.067 -13.721 -2.071 16.260 119.195
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.355e+03 1.320e+02 63.290 < 2e-16 ***
## value_lb -6.034e-03 3.215e-02 -0.188 0.851125
## countryAustralia -8.016e+01 4.208e+00 -19.047 < 2e-16 ***
## countryBrazil -5.325e+00 4.210e+00 -1.265 0.206026
## countryCanada -9.126e+01 4.205e+00 -21.701 < 2e-16 ***
## countryChile -7.385e+01 4.221e+00 -17.494 < 2e-16 ***
## countryChina 4.572e+01 4.259e+00 10.734 < 2e-16 ***
## countryColombia -5.596e+01 4.273e+00 -13.097 < 2e-16 ***
## countryEgypt 3.026e+02 4.332e+00 69.843 < 2e-16 ***
## countryEthiopia 4.240e+01 4.393e+00 9.651 < 2e-16 ***
## countryIndia 4.452e+01 4.398e+00 10.123 < 2e-16 ***
## countryIndonesia 9.397e+01 4.373e+00 21.488 < 2e-16 ***
## countryIran 7.630e+01 4.303e+00 17.734 < 2e-16 ***
## countryIsrael -7.857e+01 4.205e+00 -18.688 < 2e-16 ***
## countryJapan -1.295e+02 4.305e+00 -30.078 < 2e-16 ***
## countryKazakhstan 3.419e+02 4.256e+00 80.326 < 2e-16 ***
## countryMexico -7.859e+01 4.248e+00 -18.499 < 2e-16 ***
## countryNew Zealand -5.306e+01 4.205e+00 -12.618 < 2e-16 ***
## countryNigeria -2.818e+01 4.383e+00 -6.429 1.46e-10 ***
## countryNorway -5.865e+01 4.233e+00 -13.856 < 2e-16 ***
## countryPakistan 1.888e+02 4.359e+00 43.321 < 2e-16 ***
## countryParaguay -1.391e+01 4.239e+00 -3.280 0.001046 **
## countryPeru -1.142e+02 4.279e+00 -26.697 < 2e-16 ***
## countryPhilippines 1.072e+02 4.307e+00 24.892 < 2e-16 ***
## countryRussia 3.510e+02 4.245e+00 82.684 < 2e-16 ***
## countrySouth Africa 1.616e+01 4.255e+00 3.797 0.000149 ***
## countrySwitzerland -9.045e+01 4.219e+00 -21.438 < 2e-16 ***
## countryThailand -8.020e+01 4.314e+00 -18.591 < 2e-16 ***
## countryTurkey -9.656e+00 4.314e+00 -2.238 0.025281 *
## countryUkraine 3.599e+02 4.275e+00 84.182 < 2e-16 ***
## countryUnited Kingdom -5.004e+01 4.217e+00 -11.866 < 2e-16 ***
## countryUnited States -4.888e+01 4.219e+00 -11.587 < 2e-16 ***
## countryVietnam 4.048e+01 4.284e+00 9.449 < 2e-16 ***
## SUBJECTPIG -2.529e-02 1.493e+00 -0.017 0.986492
## SUBJECTPOULTRY 6.132e-02 1.523e+00 0.040 0.967880
## SUBJECTSHEEP -1.230e-01 1.625e+00 -0.076 0.939661
## Year -4.048e+00 6.598e-02 -61.350 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.46 on 3543 degrees of freedom
## Multiple R-squared: 0.9528, Adjusted R-squared: 0.9523
## F-statistic: 1987 on 36 and 3543 DF, p-value: < 2.2e-16Country had the biggest impact on the r-squared value meaning it explained most of the variation, with year explaining most of the remainder. Looking at the coefficients, it is obvious that countries have dramatically different trends.
Next, I repeated plots 6&7, but instead I divided the percentages by meat consumption rates instead of CVD mortality rates:
Plot 8
Model 10
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -227.30 -102.43 -35.67 49.95 454.28
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 336.983 6.289 53.58 <2e-16 ***
## value_lb -2.002 0.141 -14.20 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 145.2 on 1916 degrees of freedom
## Multiple R-squared: 0.09516, Adjusted R-squared: 0.09469
## F-statistic: 201.5 on 1 and 1916 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -243.35 -93.10 -18.35 50.63 445.45
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 263.3677 5.0568 52.082 < 2e-16 ***
## value_lb 4.2796 0.8063 5.307 1.26e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 131.7 on 1663 degrees of freedom
## Multiple R-squared: 0.01666, Adjusted R-squared: 0.01607
## F-statistic: 28.17 on 1 and 1663 DF, p-value: 1.261e-07- Both plots have p-values indicating statistical significance. The high graph had a negative coefficient, while the low graph had a positive coefficient.
Plot 9
Model 11 (high, high-medium, low, low-medium)
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -186.06 -80.37 -20.55 46.78 455.40
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 330.946 7.671 43.14 <2e-16 ***
## value_lb -1.877 0.136 -13.80 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 116 on 1019 degrees of freedom
## Multiple R-squared: 0.1575, Adjusted R-squared: 0.1567
## F-statistic: 190.5 on 1 and 1019 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -256.77 -123.33 -57.96 63.95 463.12
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 414.5378 25.0485 16.549 < 2e-16 ***
## value_lb -5.1753 0.9957 -5.198 2.5e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 171.7 on 895 degrees of freedom
## Multiple R-squared: 0.0293, Adjusted R-squared: 0.02821
## F-statistic: 27.01 on 1 and 895 DF, p-value: 2.502e-07##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -206.32 -92.62 -20.17 47.87 446.34
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 288.594 8.925 32.336 <2e-16 ***
## value_lb -9.992 5.240 -1.907 0.0569 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 134.4 on 768 degrees of freedom
## Multiple R-squared: 0.004712, Adjusted R-squared: 0.003416
## F-statistic: 3.636 on 1 and 768 DF, p-value: 0.05692##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -260.34 -89.89 -12.55 56.41 447.58
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 232.472 11.064 21.011 < 2e-16 ***
## value_lb 7.732 1.316 5.875 5.96e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 128.3 on 893 degrees of freedom
## Multiple R-squared: 0.03721, Adjusted R-squared: 0.03613
## F-statistic: 34.52 on 1 and 893 DF, p-value: 5.964e-09All the graphs except for the low graph had p-values that indicated statistical significance. The high and high-medium graphs both had a negative coefficient, however the low-medium graph had a positive coefficent.
I then decided to try splitting countries into different income brackets:
Plot 10
Model 12
- I generated a model to take a closer look:
##
## Call:
## lm(formula = deathrate ~ value_lb, data = perc_combined_test2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -181.189 -65.125 -5.169 49.131 305.830
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 277.9238 5.7782 48.099 < 2e-16 ***
## value_lb -1.1853 0.1794 -6.606 1.1e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 90.9 on 458 degrees of freedom
## Multiple R-squared: 0.087, Adjusted R-squared: 0.08501
## F-statistic: 43.65 on 1 and 458 DF, p-value: 1.095e-10- The p-value indicates statistical significance and the coefficient is slightly negative. The adjusted r-squared is again not explanatory for this graph. This indicates that as meat consumption increases, mortality decreases.
Model 13
- I divided this model and looked at each income bracket:
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -83.082 -27.974 -5.135 31.011 92.856
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 175.0484 7.2248 24.229 <2e-16 ***
## value_lb 0.1302 0.1633 0.797 0.427
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 44.33 on 114 degrees of freedom
## Multiple R-squared: 0.005542, Adjusted R-squared: -0.003181
## F-statistic: 0.6353 on 1 and 114 DF, p-value: 0.4271##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -97.787 -48.713 -1.584 49.631 107.538
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 243.2467 7.8070 31.157 <2e-16 ***
## value_lb -0.2131 0.1983 -1.075 0.285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 57.39 on 114 degrees of freedom
## Multiple R-squared: 0.01003, Adjusted R-squared: 0.001345
## F-statistic: 1.155 on 1 and 114 DF, p-value: 0.2848##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -119.114 -32.194 -4.142 22.042 135.086
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 315.3780 7.1309 44.227 <2e-16 ***
## value_lb 0.0832 0.5855 0.142 0.887
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 62.12 on 110 degrees of freedom
## Multiple R-squared: 0.0001835, Adjusted R-squared: -0.008906
## F-statistic: 0.02019 on 1 and 110 DF, p-value: 0.8873##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -187.27 -89.04 -32.27 52.64 288.82
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 297.0315 16.7322 17.752 <2e-16 ***
## value_lb -1.3174 0.7771 -1.695 0.0928 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 129.3 on 114 degrees of freedom
## Multiple R-squared: 0.02459, Adjusted R-squared: 0.01603
## F-statistic: 2.874 on 1 and 114 DF, p-value: 0.09276- My p-values indicated that none of these graphs were statistically significant, so I then split the model by subject instead:
Model 14 (Beef, Pig, Poultry, Sheep)
##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -168.84 -67.72 -4.04 45.43 300.84
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 279.1248 12.8838 21.665 <2e-16 ***
## value_lb -1.0107 0.3562 -2.837 0.0054 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 92.53 on 113 degrees of freedom
## Multiple R-squared: 0.0665, Adjusted R-squared: 0.05824
## F-statistic: 8.05 on 1 and 113 DF, p-value: 0.005396##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -175.575 -62.590 -9.487 50.685 268.590
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 296.5439 12.1035 24.501 < 2e-16 ***
## value_lb -2.1093 0.4259 -4.953 2.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 86.81 on 113 degrees of freedom
## Multiple R-squared: 0.1784, Adjusted R-squared: 0.1711
## F-statistic: 24.53 on 1 and 113 DF, p-value: 2.586e-06##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -161.347 -56.743 -6.648 51.371 285.332
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 305.0184 12.2700 24.859 < 2e-16 ***
## value_lb -1.6009 0.2837 -5.643 1.25e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 84.58 on 113 degrees of freedom
## Multiple R-squared: 0.2199, Adjusted R-squared: 0.213
## F-statistic: 31.85 on 1 and 113 DF, p-value: 1.255e-07##
## Call:
## lm(formula = deathrate ~ value_lb, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -158.51 -66.92 -12.83 50.15 311.34
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 254.8214 10.3347 24.657 <2e-16 ***
## value_lb -0.4415 0.8109 -0.544 0.587
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 95.64 on 113 degrees of freedom
## Multiple R-squared: 0.002617, Adjusted R-squared: -0.00621
## F-statistic: 0.2964 on 1 and 113 DF, p-value: 0.5872- Ths further exploration showed p-values that indicated that beef, pig, and poultry were all statistically significant, while sheep was not a statistically significant variable. All of the coefficients were slightly negative indicating that as meat consumption increases, death rates from cardiovascular disease decrease. The adjusted r-squared values were irrelevant.